Top MP David Lammy suggested leading figures could quit Labour unless Mr Corbyn backs a second referendum.
His warning comes as Labour's Brexit supremo called on Theresa May to delay Britain's departure from the EU.
Mr Corbyn is under mounting pressure to back a second referendum after the defeat of Mrs May's deal last week.
Official party policy is to seek a General Election – but if that fails, "all options" should be considered including a new referendum.
Mr Lammy insisted that after failing to trigger an election through a no-confidence vote, the leader must now campaign for a so-called "people's vote".
He said that otherwise Labour could split, leaving the party "out of power for a generation" as happened in the 1980s.
The ex-minister told Sky News: "There is a small group in our party who are so frustrated, who have so much grievance, the fear is that they are going to go off and form another party. I personally reject that.
"But the danger is that, just like 1983, a new party built around a relationship with Europe keeps the Labour Party out of power for a generation."
But in a sign of the bitter splits dividing Labour, senior backbencher Caroline Flint said the Government should rule out staying in the EU.
She told the BBC: "We should be saying, get No Deal off the table but get Remain off the table as well. So we can focus our minds on what needs to be done."
Shadow Brexit Secretary Keir Starmer today refused to back a second referendum – but claimed the Article 50 process taking us out of the EU will have to be delayed.
He said: "I think it's inevitable that Article 50 will be extended. I don't think we can get what needs to be done in the next 68 days."
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